Method for designing a die surface

ABSTRACT

A method for designing a die surface of a die, comprising generating a workpiece simulation-model corresponding to the workpiece, generating a target simulation-model corresponding to a target formed part, determining an initial die surface, which an initial numerical simulation predicts as forming the workpiece simulation-model into the target simulation-model, determining residual stresses resulting from forming the workpiece simulation-model into the target simulation-model, forming the workpiece into an actual formed part, generating a numerical representation of the actual formed part, generating an actual simulation-model, based on the residual stresses, matching the actual simulation-model and the target simulation-model, based on deviations between the matched target simulation-model and actual simulation-model, modifying the initial numerical simulation to provide a modified numerical simulation, and determining a corrected die surface, which the modified numerical simulation predicts as forming the workpiece simulation-model into the target simulation-model.

FIELD OF THE INVENTION

The present invention relates to a method and to a computer programmeproduct for forming a workpiece into an actual part by forming ansimulation-model.

BACKGROUND

A large portion of manufacturing involves producing complex shapes fromsheet metal and then joining these parts together to form a structure.These individual shapes are created mainly by a process called stamping.In the stamping process a flat sheet of metal is placed inside a die settypically consisting of male and female tools that, when closed togetherin a press, form the sheet metal to the desired shape. The die surfacesare designed using computer aided design (CAD) software and are thenmachined into the tool steel to make the dies.

The initial process of creating the die surface typically includes theuse of Finite Element Analysis (FEA) software to predict how the metalwill deform when the die is closed. This deformation includes effectslike stretching, wrinkling and spring-back.

Spring-back is particularly challenging to consider when creating diesurfaces because spring-back will cause a sheet metal part to changeshape upon removal from the die. Accounting for spring-back requiresthat the die surface be designed such that the expected spring-back willdeflect the part to the desired shape. Failure to adequately adjust forspring-back will cause problems during assembly and adversely affect thefit of parts.

Said FEA software is used to calculate the die surface shape needed toproduce the desired final shape for the component. Due to the complexbehaviour of the metal as it is being deformed when the die closes, FEAsoftware is not able to predict the correct die face shape that isneeded to actually arrive at the desired shape.

After the die is produced and during initial try out, parts are stampedand checked to see if they have the correct shape within manufacturingtolerances. If the part fails to meet specifications, then the diesurface must be reworked. This process involves making changes to thedie surface to correct regions that correspond to areas where the partis not meeting specifications. This is a mostly manual process performedby manufacturing engineers.

Typically, the parts formed in the tryout phase are measured usingmetrology equipment such as white light systems or laser scanners. Thisproduces an electronic representation of the actual manufactured part.This representation is compared to the CAD model of the desired part andareas of deviation are measured and highlighted using colours. Thesedeviations are then used to determine where and how much the die surfaceneeds to be manually adjusted to compensate for the deviation.

Generally, the deviations between the actual formed part and the idealpart (target formed part) are used to make adjustments to the diesurface design. Using experience, an engineer will tweak thesedeviations and adjust the die surfaces in the CAD software. This new dieface design is then re-machined onto the existing die.

The die try outs are repeated and a small number of parts are formed.These are again compared to the desired shape in the CAD model and ifparts do not meet specifications, the process of refining the die faceis repeated again. The average number of iterations needed to produce a“good” die face design is around four but can be as many as ten or more.Once the die face is producing parts of acceptable quality, the die isthen shipped to the stamping plant so it can be used to produceproduction parts.

While the current state of the art has been used successfully for manyyears, there are some limitations. The number of iterations needed toproduce a good die face is undefined and makes planning difficult. Eachtime the die face needs to be modified, it takes around four weeks. Thisadds significant cost and effort to producing a die and can delay thelaunch of a product.

The computation of the new die face is a manual process based onexperience. There is some trial and error involved and often the new dieface does not correct all the problems of the prior one. The need forhighly skilled engineers is also a limiting factor since it takes manyyears of experience to become expert in this process.

The use of an FE-analysis to help design the die face has improvedinitial die face quality but it is not able to fully account for thebehaviour of the metal as it deforms when the die closes. The behaviourof newer materials such as high strength steel and aluminium are evenmore difficult to predict and result in substantially longer periods oftime to iterate to an acceptable quality.

SUMMARY

The invention relates to a method for designing a die surface of a dieintended for forming a workpiece into a target formed part, comprisinggenerating a workpiece simulation-model corresponding to the workpiece,generating a target simulation-model corresponding to a target formedpart, determining an initial die surface, which an initial numericalsimulation predicts as forming the workpiece simulation-model into thetarget simulation-model, with a die having the initial die surface,forming the workpiece into an actual formed part, by measuring theactual formed part, generating a numerical representation of the actualformed part, based on the numerical representation of the actual formedpart, generating an actual simulation-model, determining residualstresses resulting from forming the workpiece simulation-model into thetarget simulation-model or the actual simulation-model, based on theresidual stresses, matching the actual simulation-model and the targetsimulation-model, based on deviations between the matched targetsimulation-model and actual simulation-model, modifying the initialnumerical simulation to provide a modified numerical simulation, anddetermining a corrected die surface, which the modified numericalsimulation predicts as forming the workpiece simulation-model into thetarget simulation-model.

Generating the actual simulation-model may comprise modifying the targetsimulation-model such that the shape of the target simulation-modeladapts to the numerical representation of the actual formed part.

The residual stresses may be determined as a plurality of stresstensors, and each stress tensor may be assigned to a location on orwithin the target simulation-model or the actual simulation-model.

Based on the stress tensors, weightings may be provided wherein eachweighting is assigned to a location on or within the targetsimulation-model or the actual simulation-model. Matching the actualsimulation-model and the target simulation-model may then be based onthese weightings.

The stress tensors and the weightings may be related in an inverselyproportional way, such that the higher a magnitude of a stress tensoris, the lower the weighting is.

Matching the actual simulation-model and the target simulation-model maycomprise determining minimal deviations between the actualsimulation-model and the target simulation-model under consideration ofthe weightings, such that the higher the weighting at a certain locationis, the closer the actual simulation-model and the targetsimulation-model are.

The target simulation-model and the actual simulation-model may eachcomprise a set of vertices, and at least one of the stress tensors andthe weightings may be assigned to the vertices of the targetsimulation-model or the actual simulation-model.

When the target simulation-model and the actual simulation-model eachcomprise a set of vertices, the deviations between the matched targetsimulation-model and actual simulation-model may be characterised by aset of vertex deviations, each vertex deviation being a positiondifference between a vertex of the target simulation-model and acorresponding vertex of the actual simulation-model.

Modifying the initial numerical simulation may comprise amendingphysical properties of the workpiece material or the target formed partmaterial.

The actual numerical representation may be a three-dimensional pointcloud.

Based on deviations between the initial die surface and the correcteddie surface, visualisations or manufacturing instructions may begenerated for transforming the initial die surface into the correcteddie surface.

The invention also relates to a computer program product with programcode being stored on a machine readable medium or embodied as anelectromagnetic wave, the program code being configured to execute thesteps: generating a workpiece simulation-model corresponding to theworkpiece, generating a target simulation-model corresponding to atarget formed part, determining an initial die surface, which an initialnumerical simulation predicts as forming the workpiece simulation-modelinto the target simulation-model, generating a numerical representationof an actual formed part, into which actual formed part a workpiece wasformed with a die having the initial die surface, based on the numericalrepresentation of the actual formed part, generating an actualsimulation-model, determining residual stresses resulting from formingthe workpiece simulation-model into the target simulation-model or theactual simulation-model, based on the residual stresses, matching theactual simulation-model and the target simulation-model, based ondeviations between the matched target simulation-model and actualsimulation-model, modifying the initial numerical simulation to providea modified numerical simulation, in particular wherein modifyingcomprises amending physical properties of the workpiece material or thetarget formed part material, and determining a corrected die surface,which the modified numerical simulation predicts as forming theworkpiece simulation-model into the target simulation-model.

With respect to the program code of the computer program product,generating the actual simulation-model may comprise modifying the targetsimulation-model such that the shape of the target simulation-modeladapts to the numerical representation of the actual formed part.

With respect to the program code of the computer program product, theresidual stresses may be determined as a plurality of stress tensors,and each stress tensor may be assigned to a location on or within thetarget simulation-model or the actual simulation-model.

With respect to the program code of the computer program product, basedon the stress tensors, weightings may be provided wherein each weightingis assigned to a location on or within the target simulation-model orthe actual simulation-model. Matching the actual simulation-model andthe target simulation-model may then be based on these weightings.

With respect to the program code of the computer program product, thestress tensors and the weightings may be related in an inverselyproportional way, such that the higher a magnitude of a stress tensoris, the lower the weighting is.

With respect to the program code of the computer program product,matching the actual simulation-model and the target simulation-model maycomprise determining minimal deviations between the actualsimulation-model and the target simulation-model under consideration ofthe weightings, such that the higher the weighting at a certain locationis, the closer the actual simulation-model and the targetsimulation-model are.

With respect to the program code of the computer program product, thetarget simulation-model and the actual simulation-model may eachcomprise a set of vertices, and at least one of the stress tensors andthe weightings may be assigned to the vertices of the targetsimulation-model or the actual simulation-model.

With respect to the program code of the computer program product, whenthe target simulation-model and the actual simulation-model eachcomprise a set of vertices, the deviations between the matched targetsimulation-model and actual simulation-model may be characterised by aset of vertex deviations, each vertex deviation being a positiondifference between a vertex of the target simulation-model and acorresponding vertex of the actual simulation-model.

With respect to the program code of the computer program product,modifying the initial numerical simulation may comprise amendingphysical properties of the workpiece material or the target formed partmaterial.

With respect to the program code of the computer program product, theactual numerical representation may be a three-dimensional point cloud.

With respect to the program code of the computer program product, basedon deviations between the initial die surface and the corrected diesurface, visualisations or manufacturing instructions may be generatedfor transforming the initial die surface into the corrected die surface.

The invention comprises the use of any numerical simulation, such as aFinite Element Analysis or other structural analyses which simulate thedeformation of featured parts and assemblies, for computing a new dieface during the try out iterations. Said numerical simulation may usemeshed models (as they are used in FE-analysis) or unmeshed models (asthey are used in new simulation approaches). In order to “learn fromevidence”, the numerical simulation uses as inputs: an electronicrepresentation of the die surface, a model of the desired part and amodel of the actual formed part from the die try outs.

The numerical simulation is used to compute the susceptibility tospring-back across the part surface. This information will be used toalign the measured actual part data to the desired part data(“matching”) in a way that isolates the effects of spring-back as bestas possible.

Then the numerical simulation may use the difference between the formedpart and the theoretical desired part to generate a feedback loop. Thisfeedback loop will “correct” the spring-back prediction in the numericalsimulation to match the behaviour demonstrated in the try out. Inparticular, the prediction is corrected or improved by modifying thephysical material properties which are used in the numerical simulation(e.g. as parameters).

The numerical simulation may then use the corrected spring-backprediction to better predict a corrected die face which would be neededto produce the desired part shape.

This “learned” correction of the numerical simulation may also be usedto improve the initial die face calculations, thus reducing the need forthe iterative changes normally required to arrive at a die face thatproduces parts of an acceptable quality.

The invention also allows an engineer to limit changes to the die faceto specific regions of the die face. This minimises the rework orre-machining of the die face by concentrating on the areas where themore significant quality problems are.

In order to provide an actual simulation-model, which represents thepart as it has been actually formed by a die surface, a targetsimulation-model of a (desired) target formed part may be fitted to anumerical representation (e.g. a measured point cloud) of the actualformed part. The actual simulation-model may also be generated directlyfrom such a numerical representation, but these directly created modelsare very different in organisation and structure compared to the meshesgenerated by numerical simulation software from the CAD model. Inparticular, said models generated from the numerical representation maybe noisy and may have missing areas of the surface that were missed inthe measurement process. A better model of the actual part is thereforeachieved by fitting the smooth and complete simulation-model of thedesired part to the measured data. However, it is not essential for theinvention how exactly the numerical representation of the actual part isutilised to generate the actual simulation-model.

When the deformation process is calculated within the numericalsimulation, residual stresses remaining in the formed part aredetermined. This may be performed with the target simulation-model orwith the actual simulation model. In a certain resolution, said residualstresses may be distributed as stress tensors all over or within thesimulation-model of the formed part. If the simulation-model is a FiniteElement (FE)-mesh, the residual stresses (or stress tensors,respectively) may be assigned to the vertices of the FE-mesh.

These residual stresses, in particular the stress tensors or magnitudesthereof, may be used as weightings for the step of matching the actualsimulation-model and the target simulation-model. The weightings mayresult from calculations or from direct deductions from the residualstresses (or stress tensors or magnitudes thereof, respectively).

Matching the actual simulation-model and the target simulation-model isan alignment process with respect to six degrees of freedom. Instead ofminimising the distance between the two models with respect to everylocation of the part, according to the invention, the determinedweightings are influencing this matching process.

In particular, this influence is realised by giving emphasis to thoseregions that have little residual stress. Lower weightings may beassigned to locations having relatively high residual stress. For thematching step, this means that the minimal deviations between the actualsimulation-model and the target simulation-model may be determined underconsideration of the weightings, which leads to the situation that thehigher the weighting at a certain location is, the closer the actualsimulation-model and the target simulation-model are in this certainlocation, and vice versa, the lower the weighting at a location is, thefurther away the actual simulation-model and the target simulation-modelare in this location.

Accordingly, the weightings and the residual stress may be relatedinversely proportionally.

The deviations that result from this matching step are then used,according to the invention, to modify the numerical simulation that hasbeen used initially. This modified numerical simulation may have amendedphysical properties of the material of the part compared to the initialnumerical simulation. Thereby, the behaviour of the part material may beamended, allowing for a better predictability of phenomena likespring-back.

With the modified numerical simulation, a corrected die surface isdetermined. The numerical simulation predicts the corrected die surfaceto form the workpiece simulation-model into the target simulation-model.

One advantage of the proposed invention is a reduction of the need forre-works: the new “learning” numerical simulation algorithm reduces thenumber of iterations to the die face by converging more quickly on theneeded shape, reducing the time to compute a new version of the die faceby eliminating the manual experienced based process of adjusting the CADmodel, allowing the user to select regions of interest where the“learning” algorithm may compute the “best” die face in these regions.The rest of the die face design would be left unchanged to minimizere-work.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention will be described in detail by referringto exemplary embodiments that are accompanied by figures, in which:

FIG. 1a-d : are cross-sectional views of two different dies in a formingprocess;

FIG. 2a-c : are cross-sectional views of the target FE-mesh and thenumerical representation of the actual formed part, wherein the figuresindicate the shape adaptation process of the former to the latter;

FIG. 3: is a cross-sectional view of the distribution of residualstresses within the formed part as computed by FE-analysis;

FIG. 4a-c : is a cross-sectional view of the actual FE-mesh and thetarget FE-mesh, wherein the figures indicate the matching process of thetwo meshes under consideration of the determined residual stresses;

FIG. 5: is a cross-sectional view of one embodiment of highlightingdeviations between the matched actual formed part and the target formedpart;

DETAILED DESCRIPTION

FIGS. 1a to 1d show two exemplary manufacturing processes of forming aworkpiece 10/10′ into an actual formed part 20/20′. In the embodiment onthe left side, which abstractly shows a conventional stamping machine,the die comprises the die surface 30. In the embodiment on the rightside, which abstractly shows a fluid forming machine, the die comprisesthe die surface 30′. The invention, however, is also compatible withother manufacturing processes as long as they relate to forming andcomprise a die with a die surface intended for forming a workpiece intoa formed part.

As indicated in FIG. 1d , in both cases residual stresses resulting fromthe forming process cause spring-back in the actual formed part 20/20′,when it is released from the die surface. The residual stresses aremostly responsible for the part deviating from the surface of the die.In particular, the present invention provides a more accurate predictionof such spring-back. Such prediction allows for designing the diesurface in such a way that the part arrives at the desired shape despitethe spring-back.

FIGS. 2a, 2b, and 2c abstractly show an exemplary process of generatingan actual simulation-model 60 based on a numerical representation of theactual formed part. The part models are shown here in a cross-sectionalview and are shaded symbolically: the meshed filling and dashed outlineindicate a FE-mesh as an exemplary target simulation-model 40, and thedots indicate a 3D point cloud as an exemplary numerical representation50).

The target simulation-model 40 may have been generated by a numericalsimulation, such as e.g. FE-analysis software. Usually, such targetsimulation-models are generated based on CAD-models of a desired(target) formed part, and then are used in a numerical simulation fordetermining a die surface which would be needed to form the targetformed part.

In case the target simulation-model 40 is embodied as a meshed FE-model,it may have a plurality of vertices (also known as nodes), which are theedges of the Finite Elements. By the shape formed by theelements/vertices, the target simulation-model 40 represents the shapeof the target formed part.

This target shape may now be fitted to a numerical representation 50 ofthe actual formed part. The numerical representation may be athree-dimensional point cloud. Such a point cloud may for example be theoutcome of a white light scan, blue light scan, laser scan or tactilemeasurement. Several different numerical representations of the samepart may be generated and be averaged. As well, numericalrepresentations may be generated for several different parts formed withthe same die surface, and be averaged. Furthermore, from numericalrepresentations of several different parts formed with the same diesurface, several different simulation-models may be generated accordingto the invention, and said several different simulation-models may beaveraged.

The target simulation-model 40 is modified until the shape of thenumerical representation 50 of the actual formed part is reached, orreached in best possible approximation within given tolerances. Thismodification may comprise shaping the target simulation-model 40, or inparticular, in case the simulation-model being embodied as FE-mesh,shifting vertices of the target FE-mesh 40 such that they best match thenumerical representation. When the form of the point cloud 50 is reached(in best approximation), the now modified (formerly: target)simulation-model becomes the actual simulation-model 60. This results ina clean simulation-model representing the actual formed part.

There may however be other ways of generating an actual simulation-modelrepresenting an actual formed part, based on a numerical representationof the actual formed part. FIGS. 2a, 2b and 2c and the correspondingdescription only render one out of many possible ways to provide anactual simulation-model.

FIG. 3 shows an abstracted cross-section of the target formed part,wherein residual stresses 70 are indicated assigned to their accordinglocations within the part. These residual stresses 70 are determinedwithin a numerical representation by simulating a deformation.

The residual stresses 70 may be defined by a plurality of stress tensorsassigned to locations on or within the simulation-model (actual ortarget). In case, the simulation-model is an FE-mesh, the tensors may beassigned to the vertices of the FE-mesh.

In the exemplary visualisation of the residual stresses according toFIG. 3 the stresses are related to a direction locally parallel orperpendicular to the part surface (plus may stand for tension and minusfor compression). A three-dimensional view of the part with avisualisation of the residual stresses may accordingly be designed as acolour map, wherein a colour tone is linked with a value.

Many different evaluations of these residual stresses may be performed,such as the calculation of averaged or non-averaged magnitudes with orwithout consideration of averaged orientations of the stress componentsof the tensors. As a consequence, weightings may be derived from theresidual stresses, which may be generally inversely related to theresidual stresses (e.g. their absolute values). These weightings maythen be used as a representative for the residual stresses in matchingthe actual simulation-model with the target simulation-model (describedin and with the FIGS. 4a, 4b, and 4c ).

The arrows 80 in FIG. 3 indicate the re-distribution of (initiallyequal) weightings to the areas where the residual stresses are low. Theweightings relate to the residual stresses in so far as they aresmaller, the larger the residual stresses are. In other words, they mayhave an—at least to some extent—inversely proportional behaviour.

FIGS. 4a, 4b, and 4c relate to said matching of the targetsimulation-model 40 and the actual simulation-model 60. The matching isperformed in any mathematical way known in the art, such that the twosimulation-models take a best fit relative to each other, according toe.g. the least square method.

However, the weightings of the vertices are thereby considered bringingthe models closer at those areas where the weightings are higher. Inthis way, the matching is performed in order to arrive at (not equal,but) adjusted minimal deviations, wherein locations within the parthaving least residual stresses are favoured when fitting. Thus, errors,i.e. deviations (see FIG. 5) between the actual and the targetsimulation-model, are shifted to the areas having most residualstresses. The simulation-models (target and actual) matched underconsideration of the weightings (which are based on the residualstresses) are shown in FIG. 4c . The deviations (FIG. 5) between theactual simulation-model and the target simulation-model depend on howthe two simulation-models are matched relative to each other. And thematching in turn depends on where the most residual stresses remain inthe formed part.

The matching may be considered being an “aligning”, i.e. bringing thesimulation-models in position relative to each other with best match.However, normally in this process equal weights are used everywherewithin the models when minimising the deviations all over. According tothe invention, the models have locally assigned individual weightingswhich are determined based on the distribution of residual stresseswithin the part.

Referring to FIG. 5, the deviations 90 resulting from the matching aredepicted with reference to a line representing the actual formed part orthe target formed part. This is one exemplary way how the deviations maybe highlighted or visualised. For every locations on the part (in acertain resolution), a position delta may be computed to provide a setof deviations, which may also be referred to as a three-dimensionaldeviation map or matrix. The deviations then are used to modify thenumerical simulation, e.g. amending the used function parametersregarding the material properties of the workpiece, or part,respectively. By this, the invention may provide better predictabilityof the consequences of residual stresses, i.e. elastic and plasticdeformation behaviour.

The initial numerical simulation is hence modified by considering thedeviations between the target simulation-model and the actualsimulation-model (which deviations depend on residual stresses). Withsuch modified numerical simulation then, a corrected die surface may bedetermined, which is predicted as forming the workpiece simulation-modelinto the target formed part simulation-model. The initial die surfacemay then be re-shaped manually or with help of NC machines to arrive atthe corrected die surface.

Although the invention is illustrated above, partly with reference tosome preferred embodiments, it must be understood that numerousmodifications and combinations of different features of the embodimentscan be made. All of these modifications lie within the scope of theappended claims.

What is claimed is:
 1. A method for designing a die surface of a dieintended for forming a workpiece into a target formed part, the methodcomprising: generating a workpiece simulation-model corresponding to theworkpiece; generating a target simulation-model corresponding to atarget formed part; determining an initial die surface, which an initialnumerical simulation predicts as forming the workpiece simulation-modelinto the target simulation-model; forming the workpiece into an actualformed part with a die having the initial die surface; generating anumerical representation of the actual formed part by measuring theactual formed part; generating an actual simulation-model based on thenumerical representation of the actual formed part; determining residualstresses resulting from forming the workpiece simulation-model into thetarget simulation-model or the actual simulation-model; based on theresidual stresses, matching the actual simulation-model and the targetsimulation-model; modifying the initial numerical simulation to providea modified numerical simulation based on deviations between the matchedtarget simulation-model and actual simulation-model, and determining acorrected die surface, which the modified numerical simulation predictsas forming the workpiece simulation-model into the targetsimulation-model.
 2. The method according to claim 1, wherein generatingthe actual simulation-model comprises modifying the targetsimulation-model such that the shape of the target simulation-modeladapts to the numerical representation of the actual formed part.
 3. Themethod according to claim 1, wherein the residual stresses aredetermined as a plurality of stress tensors, and wherein each stresstensor is assigned to a location on or within the targetsimulation-model or the actual simulation-model.
 4. The method accordingto claim 3, further comprising: based on the stress tensors, providingweightings, wherein each weighting is assigned to a location on orwithin the target simulation-model or the actual simulation-model,wherein matching the actual simulation-model and the targetsimulation-model is based on the weightings.
 5. The method according toclaim 4, wherein the stress tensors and the weightings are related in aninversely proportional way, such that the higher a magnitude of a stresstensor is, the lower the weighting is.
 6. The method according to any ofclaim 4, wherein matching the actual simulation-model and the targetsimulation-model comprises determining minimal deviations between theactual simulation-model and the target simulation-model underconsideration of the weightings, such that the higher the weighting at acertain location is, the closer the actual simulation-model and thetarget simulation-model are.
 7. The method according to any of claim 3,wherein the target simulation-model and the actual simulation-model eachcomprise a set of vertices, and wherein at least one of the stresstensors and the weightings are assigned to the vertices of the targetsimulation-model or the actual simulation-model.
 8. The method accordingto claim 1, wherein the target simulation-model and the actualsimulation-model each comprise a set of vertices, and wherein thedeviations between the matched target simulation-model and actualsimulation-model are characterised by a set of vertex deviations, eachvertex deviation being a position difference between a vertex of thetarget simulation-model and a corresponding vertex of the actualsimulation-model.
 9. The method according to claim 1, wherein modifyingthe initial numerical simulation comprises amending physical propertiesof the workpiece material or the target formed part material.
 10. Themethod according to claim 1, wherein the actual numerical representationis a three-dimensional point cloud.
 11. The method according to claim 1,further comprising: based on deviations between the initial die surfaceand the corrected die surface, generating visualisations ormanufacturing instructions for transforming the initial die surface intothe corrected die surface.
 12. A computer program product with programcode being stored on a machine readable medium, the program code beingconfigured to execute a method comprising: generating a workpiecesimulation-model corresponding to the workpiece; generating a targetsimulation-model corresponding to a target formed part; determining aninitial die surface, which an initial numerical simulation predicts asforming the workpiece simulation-model into the target simulation-model;generating a numerical representation of an actual formed part, intowhich actual formed part a workpiece was formed with a die having theinitial die surface; generating an actual simulation-model based on thenumerical representation of the actual formed part; determining residualstresses resulting from forming the workpiece simulation-model into thetarget simulation-model or the actual simulation-model; matching theactual simulation-model and the target simulation-model based on theresidual stresses; based on deviations between the matched targetsimulation-model and actual simulation-model, modifying the initialnumerical simulation to provide a modified numerical simulation; anddetermining a corrected die surface, which the modified numericalsimulation predicts as forming the workpiece simulation-model into thetarget simulation-model.
 13. The computer program product according toclaim 12, wherein generating the actual simulation-model comprisesmodifying the target simulation-model such that the shape of the targetsimulation-model adapts to the numerical representation of the actualformed part.
 14. The computer program product according to claim 12, 15.wherein the residual stresses are determined as a plurality of stresstensors, and wherein each stress tensor is assigned to a location on orwithin: the target simulation-model or the actual simulation-model, andwherein the program code is further configured to: based on the stresstensors, providing weightings, wherein each weighting is assigned to alocation on or within: the target simulation-model or the actualsimulation-model, wherein the stress tensors and the weightings arerelated in an inversely proportional way, such that the higher amagnitude of a stress tensor is, the lower the weighting is, whereinmatching the actual simulation-model and the target simulation-model isbased on the weightings.
 16. The computer program product according toclaim 14, wherein matching the actual simulation-model and the targetsimulation-model comprises determining minimal deviations between theactual simulation-model and the target simulation-model underconsideration of the weightings, such that the higher the weighting at acertain location is, the closer the actual simulation-model and thetarget simulation-model are.